15.04.21

Giles Gardam

15:45-17:30

Three conjectures on group rings of torsion-free groups are commonly attributedto Kaplansky, namely the unit, zero divisor and idempotent conjectures. Forexample, the zero divisor conjecture predicts that ifKis a field andGis atorsion-free group, then the group ringK[G]has no zero divisors. I will surveywhat is known about the conjectures, including their relationships to eachother and to other conjectures and group properties, and finish with my recentcounterexample to the unit conjecture.